More warnings about a shortage of STEM graduates. Where are these messages coming from? There is no shortage, many graduates in engineering for example are forced to work in jobs that are nothing to do with their degrees, or even worse they are in non-graduate jobs.

Engineering needs to emphasise its creative side to encourage more young people to take it up as a career.

Sir John O’Reilly

This is fine. The fields of science and engineering do require some creative thinking. There is an element are art to this.

But I am worried about the continual message of a lack of STEM graduates where in reality many are unemployed. I really don’t understand the B.S. here.

Schools watchdog Estyn says too many pupils struggle with the basics of mathematics and maths skills were “at best, average” in more than half of schools inspected in Wales last year.

The mathematics skills and the teaching methodologies in Welsh schools seems to be a continuing source of worry.

The attitude that it is okay to not be good at basic mathematics needs to change. There is some social acceptability in being poor in mathematics. I am sure that when English teachers, lets say at a party, explain that they are English teachers are not met with a funny look and the response “I hated English at school and I cannot read or write”…

Quite regularly one will come across a website, blog or some thread on a forum that says the gravity is just electromagnetism. For sure they are not the same. However, I am not sure what would constitute the ‘nail in the coffin’ for all these clams.

With this in mind, I am not going to try to debunk every such claim. However, I think the reason for this seeming equivalence comes from the static limit. In this limit it is true that there are many formal similarities between Newtonian gravity and electrostatics. In fact there are many formal similarities in the full classical theories, both are very geometrical in nature, but I won’t go into details here.

I just wanted to point out one very clear difference between gravity and electromagnetism that can be seen in this static limit. That is the lack of a generalisation of the equivalence principal for electromagnetic theory. This principal in gravity is very important and one that I will comment on in due course.

The static limit
I am guessing that we have all seen Coulombs law for electrostatics and Newton’s law for gravity. Let me just write them down

$latex F = k \frac{qQ}{r^{2}}$,

where $latex k$ is Coulombs constant, it is a measure of the strength of the electrostatic force and $latex q$ and $latex Q$ are the electric charges of two point particles. The above expression is the electrostatic force between two such charged particles.

Similarly we have Newton’s law of gravity

$latex F = G \frac{mM}{r^{2}}$,

where $latex G$ is Newton’s constant which measures the strength of the gravitational force and $latex m$ and $latex M$ are the masses of two point particles. The above expression measures the gravitational force between these particles.

These expressions for the forces should be seen as the static non-relativistic limit. I just mean that as long as the particles are moving slow enough then the change in the fields can be viewed as instantaneous. This is okay for many applications, but it is not the full picture. However, it is the one you see at high school.

The formal similarities at this level are clear. You just need to swap constants and interchange charge and mass. But this does not mean they are the same, and there is a subtle issue here. Before that we need Newton’s law of motion

Newton’s second law
Newton’s second law tells us that the force exerted on a particle is proportional to the acceleration of that particle. Moreover, the constant of proportionality is the (inertial) mass.

$latex F = m a $.

That is all we will need.

The gravitational equivalence principal
Let us think of the particle of mass $latex m$ as a test particle. That is we will think of how it is moving in the gravitational field generated by the particle $latex M$ and that it does not generate a gravitational field of its own. This approximation is good for small objects moving in the gravitational field of big objects; say planets around a star or satellites in orbit around the Earth.

Now we can examine how the small mass is influenced by the big mass. We should just equate the two expressions due to Newton

$latex ma = G \frac{mM}{r^{2}} $,

for which we can solve for the acceleration

$latex a = G \frac{M}{r^{2}}$.

We notice a very amazing thing. The small mass cancels from both sides of the equation. (We assume that gravitational mass and inertial mass are the same. This seems to be case in nature.)

This means that the motion of the test particle does not care about any of the intrinsic properties of that particle. The only things it does care about is the initial position and velocity. This is one form of the equivalence principal which has it’s roots in the experimental work of Galileo- acceleration of a test particle due to gravity is independent of the mass being accelerated.

Thus, really all the information about the test particles motion is encoded in the gravitational field alone. All test particles whatever their mass will behave the same. This is the clue that gravity can be formulated very intrinsically in terms of space-time geometry alone; this leads to general relativity which is not the subject for today.

The electromagnetic version
Now let us play the same game with electrostatics…

$latex ma = k \frac{q Q}{r^{2}} $,

where we think of the test particle $latex (m, q)$ moving in the electric field generated by the particle $latex (M,Q)$. Now solving for the acceleration gives us

$latex a = k \left(\frac{q}{m}\right) \frac{Q}{r^{2}} $.

Now we see the difference. The motion of the test particle does depend on the intrinsic properties of that particle, namely the charge-mass ratio. There is no similar statement like for gravitational physics; there is no equivalence principle.

Closing remarks
Everything above is done in a particular limit of the full classical theories. The same picture is true when we examine the motion of test particles in general relativity and the Lorentz force in electromagnetic theory. I have chosen these limits because I think this is clear and also the source of the instance that gravity is just electromagnetic theory. I have pointed out one clear and explicit difference.

One can do the same with Coulomb’s law for the magnetic force. Although magnetism is a bit more complicated we can examine the situation for point-like poles. This is okay for small enough poles that are well separated. You will reach the same conclusion that there is no equivalence principal in this situation. Thus, gravity is not magnetism either.

On Friday 7th November I will be giving a short talk to physics students entitled ‘Fermions in Physics: from anticommuting variables to supermanifolds’, as part of the Ogólnopolska Sesja Kół Naukowych Fizyków.

This translates as ‘Scientific Session of the Nationwide Circle of Physicists’. This year the session is in the Tricity area.

I hope to tell them a little about the passage from the canonical anticommutation relations to Grassmann algebras and then supermanifolds. I have 45mins to get them interested in this geometric side of mathematical physics.

I will post the slides here after the event, but they may not make much sense without me telling this you this story.

There is always some worry that government cut backs will effect the status of UK science. The latest warning comes from the Campaign for Science and Engineering (CaSE) which represents 100 scientific bodies and businesses.

If you look at what other countries are doing they are investing heavily. They are all going upward. Unfortunately the UK’s (investment) is going downwards.

Dr Sarah Main Director, Case speaking to the BBC.

The UK government has invested less in science than the European Union average for many years. The EU average rose from 2.04% of GDP in 2011 to 2.07% of GDP in 2012. The UK investment dropped from 1.78% to 1.72% of GDP.

This makes me worry about the UK loosing its place in science, though like make things for a small country we punch above our weight. I just hope we can continue to do so in science. Moreover, this downwards trend on funding is worrying for science students and especially PhD students. The situation with postdoc positions is difficult enough without further erosion of UK science.

English today is the main language of science across the globe. It has not always been like that, a mixture of English, French and German in about equal proportions was the norm in the 19th century. Before that Latin was the language used across western Europe; from the late medieval period to the mid-17th Century.

It may be no surprise that German was cast out as a common scientific language after the first world war. It is not that English rose to the top of the pile, but rather than German was cut down. Then after the second world war the United States of America became a leading scientific power and that for sure influenced the choice of international language.

Almost of today’s scientific discoveries will be published in English. Moreover, English seems to be the language that scientists who do not share a common mother tongue will use. For example, here in Warsaw international visitors will tend to use English when conversing with Polish researchers.

You can find out more details about the rise on English via the link below.

I don’t find it at all easy to write papers or lectures notes, even if the hard work of getting all the material together has been done. To help with the procrastination I may try out the ideas of the writers linked to below.

I am not sure exactly how my fellow mathematicians sharing the office will react though…

Here is my list of Polish food that I have enjoyed in Warsaw. In no particular order

Kashanka

Polish blood sausage made with pig’s blood and buckwheat. It is like a cross between a haggis and a black pudding. It can be boiled, grilled or fried. Very delicious, I had one from a BBQ recently.

Biała kiełbasa

The domestic or common white sausage. To be found in every food shop in Poland. Best grilled or fired. The meat filling is more coarse than the typical British banger and contains cubes of fat. May not be the best for your waist, but you will enjoy it.

Ogórek kiszony/kwaszony

There are (at least) two kinds of dill pickles in Poland. Ogórek kiszony are pickles preserved in wooden barrels. They are a little salty and the taste can change as they mature. I like the mature ones that have started to lose their colour. Very very popular in Poland.

The second kind ogórek konserwowy is preserved in vinegar. Also very good and nothing like the British gherkins that are far too sour.

Kapusta

The word mean cabbage, though it commonly will refer to the Polish version of sauerkraut. It has a distinctive sour taste and does very well with any of the above. Generally I would say that it is more palatable that the German versions and that you should seek it out in the Polish section of the supermarket.

Sznycel (Kotlet Mielony)

This is a flattened cutlet of port that is breaded and then fried. Very delicious and goes great with fries for lunch. They do a great sznycel in a restaurant near my flat.

Kaczka Pieczona z Jabłkami

Roast duck with apples, it can also be served with a beetroot mash and a red berry sauce. This is my wife’s favourite. You really have to try this in a restaurant in Warsaw, I insist.

Befsztyk tatarski

Polish style stake tartare, not to everyone’s taste, but here in Warsaw it is popular. It should be served with finely chopped ogórek, chopped preserved mushrooms and onions. Often it will also come with a small piece of fish to mix in and a drop of olive oil. I also like to add a little Maggi seasoning sauce to mine. I recommend it and you can buy packs of the tartare in the supermarkets in Poland to enjoy at home. That said, it is great for a starter in the restaurants here.

Bigos

Polish hunter’s stew, made with kapusta, various cuts of meat and sausages, mushrooms and dried plums. Very good and should be eaten if you get the chance. However, avoid the ready made versions in jars that you can find today. It is best eaten in a small restaurant in Warsaw.

That is just a flavour of the great food you can get in Poland. Maybe I should look at Polish deserts next week…

The 2014 Nobel prize in physics has been awarded to Isamu Akasaki, Hiroshi Amano and Shuji Nakamura for the development of blue LEDs.

This year’s Nobel Laureates are rewarded for having invented a new energy-efficient and environment-friendly light source – the blue light-emitting diode (LED). In the spirit of Alfred Nobel the Prize rewards an invention of greatest benefit to mankind; using blue LEDs, white light can be created in a new way. With the advent of LED lamps we now have more long-lasting and more efficient alternatives to older light sources.

Notes for Linear algebra 2400-FIM1AL

About the author

My name is Andrew Bruce and I am a mathematical physicist who works on the boundaries of physics and modern geometry.

Currently I am an Assistant Professor in the Department of Mathematical Physics and Differential Geometry, IMPAN , Warsaw, Poland.

My research interests are in mathematical physics and modern geometry. In particular I have been interested in supermanifolds, graded manifolds, Lie algebroids and various generalisations of Poisson structures.

I am also an online tutor in physics and mathematics at Pembrokeshire College.